Three-dimensional zeropotent algebras over an algebraically closed field of characteristic two

2019 ◽  
Vol 48 (4) ◽  
pp. 1613-1625
Author(s):  
Kiyoshi Shirayanagi ◽  
Yuji Kobayashi ◽  
Sin-Ei Takahasi ◽  
Makoto Tsukada
Keyword(s):  
Three Dimensional ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Characteristic Two

scholarly journals Geometric Weil representation in characteristic two

2011 ◽  
Vol 11 (2) ◽  
pp. 221-271 ◽  
Author(s):  
Alain Genestier ◽  
Sergey Lysenko
Keyword(s):  
Weil Representation ◽  
Closed Field ◽  
Triangulated Category ◽  
Algebraically Closed Field ◽  
Witt Vectors ◽  
Suitable Sense ◽  
Characteristic Two ◽  
Greenberg Realization ◽  
Geometric Analogue

AbstractLet k be an algebraically closed field of characteristic two. Let R be the ring of Witt vectors of length two over k. We construct a group stack Ĝ over k, the metaplectic extension of the Greenberg realization of $\operatorname{\mathbb{S}p}_{2n}(R)$. We also construct a geometric analogue of the Weil representation of Ĝ, this is a triangulated category on which Ĝ acts by functors. This triangulated category and the action are geometric in a suitable sense.

scholarly journals THE 2-RANKS OF HYPERELLIPTIC CURVES WITH EXTRA AUTOMORPHISMS

2009 ◽  
Vol 05 (05) ◽  
pp. 897-910 ◽  
Author(s):  
DARREN GLASS
Keyword(s):  
Automorphism Group ◽  
Hyperelliptic Curve ◽  
Hyperelliptic Curves ◽  
Closed Field ◽  
Base Field ◽  
Characteristic P ◽  
Algebraically Closed Field ◽  
Characteristic Two ◽  
Carry Over ◽  
The Relationship

This paper examines the relationship between the automorphism group of a hyperelliptic curve defined over an algebraically closed field of characteristic two and the 2-rank of the curve. In particular, we exploit the wild ramification to use the Deuring–Shafarevich formula in order to analyze the ramification of hyperelliptic curves that admit extra automorphisms and use this data to impose restrictions on the genera and 2-ranks of such curves. We also show how some of the techniques and results carry over to the case where our base field is of characteristic p > 2.

scholarly journals GENERAL HYPERPLANE SECTIONS OF THREEFOLDS IN POSITIVE CHARACTERISTIC

2018 ◽  
Vol 19 (2) ◽  
pp. 647-661 ◽  
Author(s):  
Kenta Sato ◽  
Shunsuke Takagi
Keyword(s):  
Projective Variety ◽  
Positive Characteristic ◽  
Hyperplane Section ◽  
Three Dimensional ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Double Points ◽  
Canonical Singularities ◽  
Hyperplane Sections

In this paper, we study the singularities of a general hyperplane section $H$ of a three-dimensional quasi-projective variety $X$ over an algebraically closed field of characteristic $p>0$. We prove that if $X$ has only canonical singularities, then $H$ has only rational double points. We also prove, under the assumption that $p>5$, that if $X$ has only klt singularities, then so does $H$.

scholarly journals Invariants of the dihedral group D2p in characteristic two

2011 ◽  
Vol 152 (1) ◽  
pp. 1-7 ◽  
Author(s):  
MARTIN KOHLS ◽  
MÜFİT SEZER
Keyword(s):  
Upper Bound ◽  
Dihedral Group ◽  
Explicit Description ◽  
Closed Field ◽  
Generating Set ◽  
Algebraically Closed Field ◽  
Finite Dimensional ◽  
Characteristic Two ◽  
Minimal Generating Set

AbstractWe consider finite dimensional representations of the dihedral group D2p over an algebraically closed field of characteristic two where p is an odd prime and study the degrees of generating and separating polynomials in the corresponding ring of invariants. We give an upper bound for the degrees of the polynomials in a minimal generating set that does not depend on p when the dimension of the representation is sufficiently large. We also show that p + 1 is the minimal number such that the invariants up to that degree always form a separating set. We also give an explicit description of a separating set.

scholarly journals Belyi’s theorem in characteristic two

2019 ◽  
Vol 156 (2) ◽  
pp. 325-339 ◽  
Author(s):  
Yusuke Sugiyama ◽  
Seidai Yasuda
Keyword(s):  
Rational Function ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Characteristic Two ◽  
Obstruction Class

We prove an analogue of Belyi’s theorem in characteristic two. Our proof consists of the following three steps. We first introduce a new notion called pseudo-tameness for morphisms between curves over an algebraically closed field of characteristic two. Secondly, we prove the existence of a ‘pseudo-tame’ rational function by showing the vanishing of an obstruction class. Finally, we construct a tamely ramified rational function from the ‘pseudo-tame’ rational function.

Classification of three-dimensional zeropotent algebras over an algebraically closed field

2017 ◽  
Vol 45 (12) ◽  
pp. 5037-5052 ◽  
Author(s):  
Yuji Kobayashi ◽  
Kiyoshi Shirayanagi ◽  
Sin-Ei Takahasi ◽  
Makoto Tsukada
Keyword(s):  
Three Dimensional ◽  
Closed Field ◽  
Algebraically Closed Field

scholarly journals Oort groups and lifting problems

2008 ◽  
Vol 144 (4) ◽  
pp. 849-866 ◽  
Author(s):  
T. Chinburg ◽  
R. Guralnick ◽  
D. Harbater
Keyword(s):  
Finite Groups ◽  
Characteristic Zero ◽  
Positive Characteristic ◽  
Closed Field ◽  
Projective Curve ◽  
Smooth Projective Curve ◽  
Algebraically Closed Field ◽  
Cyclic Groups ◽  
Characteristic Two ◽  
Field Of Positive Characteristic

AbstractLet k be an algebraically closed field of positive characteristic p. We consider which finite groups G have the property that every faithful action of G on a connected smooth projective curve over k lifts to characteristic zero. Oort conjectured that cyclic groups have this property. We show that if a cyclic-by-p group G has this property, then G must be either cyclic or dihedral, with the exception of A4 in characteristic two. This proves one direction of a strong form of the Oort conjecture.

ON THE BASE-POINT-FREE THEOREM OF 3-FOLDS IN POSITIVE CHARACTERISTIC

2014 ◽  
Vol 14 (3) ◽  
pp. 577-588 ◽  
Author(s):  
Chenyang Xu
Keyword(s):  
Line Bundle ◽  
Positive Characteristic ◽  
Three Dimensional ◽  
Base Point ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Big Line Bundle

Let $(X,{\rm\Delta})$ be a projective klt (standing for Kawamata log terminal) three-dimensional pair defined over an algebraically closed field $k$ with $\text{char}(k)>5$. Let $L$ be a nef (numerically eventually free) and big line bundle on $X$ such that $L-K_{X}-{\rm\Delta}$ is big and nef. We show that $L$ is indeed semi-ample.

scholarly journals The strong simple connectedness of tame algebras with separating almost cyclic coherent Auslander–Reiten components

2021 ◽  
Author(s):  
Piotr Malicki
Keyword(s):  
Closed Field ◽  
Algebraically Closed Field ◽  
Main Application ◽  
Finite Dimensional ◽  
Simple Connectedness ◽  
Tame Algebras

AbstractWe study the strong simple connectedness of finite-dimensional tame algebras over an algebraically closed field, for which the Auslander–Reiten quiver admits a separating family of almost cyclic coherent components. As the main application we describe all analytically rigid algebras in this class.

scholarly journals On Unramified Separable Abelian p-Extensions of Function Fields I

1959 ◽  
Vol 14 ◽  
pp. 223-234 ◽  
Author(s):  
Hisasi Morikawa
Keyword(s):  
Galois Group ◽  
Function Field ◽  
Function Fields ◽  
Abelian Extension ◽  
Closed Field ◽  
Jacobian Variety ◽  
Algebraically Closed Field

Let k be an algebraically closed field of characteristic p>0. Let K/k be a function field of one variable and L/K be an unramified separable abelian extension of degree pr over K. The galois automorphisms ε1, …, εpr of L/K are naturally extended to automorphisms η(ε1), … , η(εpr) of the jacobian variety JL of L/k. If we take a svstem of p-adic coordinates on JL, we get a representation {Mp(η(εv))} of the galois group G(L/K) of L/K over p-adic integers.

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